jmc

We notice immediately that both terms are divisible by $5$: $2835=5\cdot 567$ and $8960=5\cdot 1792$. Repeatedly dividing 1792 by 2, we find that $1792/2^8=7$, so $8960=2^8\cdot 5\cdot 7$. At this point, we are almost done: we know that $2$ does not divide into $2835$, so the only other factor we need to check is $7$. Since $2835=28\cdot 100+35$ is clearly divisible by $7$, then the greatest common factor is $5\times 7=\boxed{35}$.